Frequently asked questions

Can you make a map with such-and-such a color scheme? I'm kind
of busy at the moment, so I'm probably not going to be making a lot more
maps. However, you can easily make maps with other color schemes yourself.
It's easy to take the purplemaps, separate out the blue and red
channels, and then remap them any way you like. This is just a couple of
clicks in Photoshop. (In fact, I used the excellent free Photoshop clone
Gimp for my image manipulation, which does the job very well. You can
download it from here.)

Can you make a map showing such-and-such data? Many people have
asked for maps showing number of people who voted, number of registered
voters, differences between the candidates' votes, and all sorts of other
things. Once again, I'm probably not going to be doing this soon, but I
certainly encourage others to make such maps. My software for creating
cartograms is freely available for download here.

Do you have maps for previous elections? Yes. There are maps
for the 2004 and 2006
elections. None before that – sorry.

Where are Alaska and Hawaii? Not on the maps. I know. Sorry.
There are some technical problems with non-contiguous cartograms that make
it difficult to produce nice maps. But I'm working on it. Stay tuned.

The shapes of the cartograms look different from those for the
previous election. What's up with that? It's true the shapes are a bit
different even though the population data used are the same. The reason is
that I've made some improvements to the computer algorithm in the last
couple of years. The old algorithm tended to create a "bloated" look when
coastal regions like Florida had large populations – they would
expand like balloons and become bulbous. In the new version of the
algorithm such regions retain their overall shape better and there is less
bloating. Compare Florida in the 2004 and 2008 maps to
see what I mean.

Can I use your figures in my magazine, newspaper, mailing list, web
page, artwork, wall hanging, interpretive dance, etc? Absolutely. The
maps and the accompanying text are released under a Creative Commons
License that allows for their free distribution and use in derivative
works. I would appreciate hearing from you if you wish to make use of
them, but it is not required under the terms of the license.

How exactly do you make these maps? So you want the technical
stuff, huh? OK, well, let's see. The cartograms were made using the diffusion
method of Gastner and Newman. The population data and geographic
boundaries were taken from the most recent (year 2000) US Census.

The calculation of the cartograms involves allowing the population to
diffuse in the two-dimensional space of the map, carrying the boundaries of
the states or counties with it, until it reaches a uniform equilibrium.
The diffusion equation is integrated in Fourier space, where it takes a
particularly simple form: the initial density function is evaluated on a
4608x3072 lattice, transformed using a two-dimensional fast Fourier
transform, convolved with a Gaussian kernel and then back-transformed to
give the diffusion field at an arbitrary later time. I used closed
(Neumann) boundary conditions at the edges of the map, meaning that the
Fourier transform in this case is a discrete cosine transform.

The diffusion field is then used to calculate the diffusion velocity as a
function of position and the velocity integrated over time to give the
displacement of the map features. The integration is performed using a
fourth-order Runge-Kutta integrator with an adaptive step size and local
extrapolation. The entire calculation took about ten minutes for each map
on a standard desktop computer running the Fedora Linux operating system. The
basic images were created using a specially written rendering program and
some artistic refinements were added using Gimp, a free image manipulation program.

Have these maps been getting press coverage? The maps I and two
colleagues made for the 2004 election have received wide attention, and
were used as part of the 2008 election night coverage on ABC and on the BBC
in Britain. They have also appeared in the Washington Post, on CNN
Headline News, in The Guardian, and on Salon.com among other places. You
are welcome to use any of the maps in your publication as well; see above
for the licensing details.

Mark Newman, Department
of Physics and Center for the Study of Complex Systems, University of
Michigan
Updated: November 7, 2008